Schools Chancellor Rudy Crew went on the offensive last night, warning Mayor Giuliani that their bitter feud is hurting schoolkids and vowing that “I’m not going to let anybody run me out of town.”

While Giuliani was on a political trip to Los Angeles for his presumed Senate campaign, the beleaguered schools chancellor went on television to counter the mayor’s onslaught against the school system.

“The handwriting is on the wall that we better figure out how we’re going to get this thing back to right or, otherwise, our children will suffer,” Crew said during a 40-minute interview on New York 1’s “Inside City Hall.”

Earlier in the day, Giuliani again took credit for most of the reforms in the school system during Crew’s tenure.

“Because if I didn’t put the pressure on for that to occur, all of you know that this discussion would not be taking place,” he told reporters.

Crew scoffed at the mayor’s claim.

“I don’t want to be disrespectful in any way. I just know that it’s a sad state of affairs when a person has to believe that they’ve done everything,” said Crew, who included his predecessor, Ramon Cortines, among those who have helped the system.

Crew went on to say that he hopes Giuliani “would believe that somebody who has been doing this work for 30 years or so, versus someone who as a politician has just sort of entered the conversation about it, that there’s a difference in the quality of the input and the quality of knowledge that I can provide.”

The feud between Giuliani and Crew – once the closest of allies – erupted earlier this year when Crew threatened to quit after learning the mayor was lobbying Board of Education members to support his plan for school vouchers.

And last month, Giuliani began his strident attacks on the school system, saying the Board of Education should be “blown up.” Crew infuriated the mayor when he fired off a letter accusing him of engaging in “rhetoric of destruction.”

“At this point, we don’t have a relationship,” Crew said. “I don’t know any other way to characterize it. I have no opportunity other than through my once-a-week meetings to basically have any conversation with the mayor.”

Meanwhile, Giuliani forged ahead with his voucher proposal. He is planning a trip next week to Milwaukee to get a firsthand look at the controversial program that sends kids to private schools with public money.

In Milwaukee, where 6,000 kids are in the voucher program, he will meet Mayor John Norquist and visit one of the 86 participating private schools.

The Milwaukee visit comes on the heels of yesterday’s trip to Chicago by Giuliani’s senior adviser, Tony Coles. Both trips are part of new fact-finding missions to out-of-state school districts by the mayor and his staff.